Question

A (3x3) mateix A has Trace (A)=-2 Trace (A²) = 30 Trace (A^3) =- 116.
Find the determinant of A​

Answer 1

Answer:

Let A be a 3×3 matrix with real entries such that det(A)=6 and tr(A)=0. If det(A+I)=0 (I denotes 3×3 identity matrix), then the eigenvalues of A are:

(i) −1,2,3;

(ii) −1,2,−3;

(iii) 1,2,−3;

(iv) −1,−2,3.

If a,b,c are 3 eigenvalues then a+b+c=0 and abc=6 because sum of eigen values is trace and product is the determinant value. Then how to apply det(A+I)?